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 Question from a student: find the maximum volume of a cone if the sum of it height and volume is 10 cm.

Hi,

I think you mean

find the maximum volume of a cone if the sum of it height and radius is 10 cm.

The volume $V$ of a cone in cubic centimeters is given by

$V = \frac13 \pi \; r^2 h$

where $r$ is its radius and $h$ is it height, both in centimeters. You know that the sum of $r$ and $h$ is 10 cm so this allows you to write the volume $V$ as a function of one variable. Use the calculus you know to maximize this function.

Penny

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